Writing the Judge will do nothing. You should have either asked for a new trial if that was allowable, or appealed his Judgment if a final Judgment. I do not know at what stage of your suit it was dismissed, but since it was "with prejudice", any attempt to re-file the same suit will result in an exception of res judicata. So, you need to appeal, and your Lawyer should know how and the time period for your situation.